Geometric quantities of lower doubly excited bound states of helium

Abstract

Expectation values of single electron and interelectronic geometric quantities such as 〈r〉, 〈r 12〉, 〈r <〉, 〈r >〉, 〈cosθ 12〉 and 〈θ 12〉 are calculated for doubly excited 2pn p1 P e (3 ≤ n ≤ 5), 2pn p3 P e (2 ≤ n ≤ 5) and 2pnd1,3 D° (3 ≤ n ≤ 5) states of helium using Hylleraas-B-spline basis set. The energy levels converge to at least 10 significant digits in our calculations. The extrapolated values of geometric quantities except for 〈θ 12〉 reach 10 significant digits as well; 〈θ 12〉 reaches at least 7 significant digits using a multipole expansion approach. Our results provide a precise reference for future research.